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Particle flow numerical simulation software (PFC^{3D}) was utilized to establish the consolidated-undrained triaxial compression test numerical models of mine tailings with different dry densities to deeply investigate the macroscopic and microscopic characteristics of mine tailings in a tailing pond in Hunan Province. Comparing the results of the simulation and the laboratory experiment, the mesoscopic parameters of the particle flow numerical simulation were obtained through continuously adjusting the mesoscopic parameter with the higher degree of agreement between the stress-strain curve, the peak strength, and the elastic modulus as the determining standard. The macroscopic and microscopic characteristics of mine tailings were studied from the perspectives of stress-strain, axial strain-volume strain, coordination number, particle velocity vector, and contact force between particles. After numerous numerical tests, it was found that the PFC^{3D} simulation results are consistent with experiment results of the dry density tailing samples under different confining pressures; compared with the high confining pressure, the simulation test results at lower confining pressures were more with that of the laboratory tests; low density and high confining pressure both have inhibitory effect on the dilatancy characteristics of triaxial samples; with the same confining pressure, the dilatancy tendency of low dry density samples is suppressed comparing with the high dry density samples. The initial coordination number of the numerical model is large, which proves that the contact degree of the model is good to some extent.

Tailings are complex geotechnical materials whose mechanical properties are greatly affected by various factors. As the main material of the tailing dam, the mechanical properties of the tailings exhibit great relevance with the safe operation of the tailing dam. Therefore, it is of great practical significance of studying the tailing mechanical properties. Under the load, the deformation of the tailing structure is mainly determined by its structural strength and modulus, while the structural strength and modulus are mainly determined by the size, shape, and arrangement of its particles, that is, the macroscopic deformation and failure of the tailing structure resulted from its fine and microstructure changes. In geotechnical and rock materials studies, many scholars at home and abroad have paid great attention on researching it from the perspective of discrete element particle flow [^{2D} and studied the effect of the change of mesoparameters on the strength of the specimen under the parallel bonding model. A series of PFC numerical experiments were conducted by Yang and Han [^{2D} software. He bundled the basic particles belonging to the same particle to obtain a sample that can be crushed and carried out many direct shear simulation tests. It was found that the degree of particle crushing exhibited influence on the shear expansion characteristics of coarse-grained soil and the internal friction angle. Luo et al. [^{2D} to numerically simulate the sand biaxial test, and their results showed that the particle flow numerical simulation test can effectively simulate the formation and development of sand shear bands mechanism. Shen et al. [^{3D} particle flow program to numerically simulate the direct shear test of sand under different vertical pressures and explain the phenomenon of sand dilatation at a mesoscopic point of view. Based on the spherical particles in PFC, Yang and Li [^{2D} to study the size effect of the large triaxial sample, suggesting that scaling the sample by the equal mass substitution method was finite but could not be infinitely reduced. Yin et al. [^{2D} and found that the friction angle between the sand and that between the particles could be approximated as an inclined line, and the cohesive force and the contact strength of the particles obeyed the linear law as well approximately.

There are relatively numerous researches about sandy soil, coarse grained soil, and rock materials, but few studies on tailings. In addition, the nonbonded linear contact model is used in most of above studies, and some are exploring through the direct shear test. Compared with the triaxial test, the direct shear test artificially defines the location of the shear failure surface, while that of triaxial test shear is along the weakest surface of the specimen. Based on the laboratory triaxial test results of tailings specimen, this paper compares the simulation results with the laboratory test results, and by continuously adjusting the parameters with the higher degree of agreement between the stress-strain curve, the peak strength, and the elastic modulus as the determining standard. The microstructure characteristics of tailings were analyzed from the perspective of coordination number, particle velocity vector, and particle displacement field. The method obtains parameters that are not easily obtained in laboratory tests.

The tailings used in this test were taken from a tailing pond in Hengyang, Hunan Province, and the grading parameters of the samples obtained by sieving are shown in Table

Particle composition parameters of tailings.

Particle composition parameters | ||||
---|---|---|---|---|

Effective diameter ( |
Median size ( |
Constrained size ( |
Coefficient of nonuniformity ( |
Coefficient of curvature ( |

0.0780 | 0.1620 | 0.2000 | 2.5320 | 1.6610 |

Samples before and during loading.

LH-TTS series automatic triaxial apparatus were employed with the maximum axial loading force of 10 kN at the loading rate ranging between 0.0001 and 4.8 mm/min. The process of triaxial loading is controlled by a computer, and the axial strain of the sample reaches 15% as the termination condition of loading. The consolidated-undrained triaxial compression test was carried out for each specific dry density sample with the loading rate of 0.6 mm/min at a confining pressure of 100 kPa, 200 kPa, and 300 kPa, respectively. The test data was automatically collected and collated by the computer, and Figure

Automatic triaxial apparatus

Excess pore water pressure has been the main cause of many engineering accidents. The increase of excess pore water pressure would lead to the decrease of the equivalent axial and radial effective principal stresses as well as the diameter of the Mohr circle to be unchanged and shifting to the left, causing soil instability and destruction [

Relationship between pore water pressure and axial strain.

Dry density is 1.53 g/cm^{3}

Dry density is 1.61 g/cm^{3}

Dry density is 1.66 g/cm^{3}

From Figures ^{3} and 1.66 g/cm^{3}, dilatancy happened on all the samples with confining pressure of 100 kPa (limited to space, the relationship between stress and strain in the laboratory test was not discussed separately).

If the model is generated according to the original gradation of the sample, millions of spherical particles will be required. In order to avoid generating more particles when generating the numerical model of the triaxial test, resulting in longer calculation time, the original gradation of the sample cannot be used directly. Ning [

In the simulation test of the particle flow of sandy soil, the contact method chosen by most researchers is the nonbonded contact [

Linear contact bond model (from PFC5.0).

According to the determined model size and particle size, linear bonding contact was set between the spherical particles, and the cylinder command was utilized to generate the uncovered cylindrical side wall of the particle flow triaxial test model. To reduce the calculation time of wall generation, the plane command was utilized to create a plane rigid wall at the top and bottom of the specimen. To ensure the uniformity of the generated model, the friction coefficient of the wall is 0 [

Model of the particle flow numerical simulation.

During the PFC simulation process, the confining pressure is provided by the top and bottom plane rigid walls and the flexible wall with uncover cylindrical side wall in the initial consolidation stage before loading; the confining pressure is only provided by the flexible uncovered cylindrical side wall during the loading stage. The confining pressure and the axial pressure were adjusted by controlling the movement speed of the cylindrical side flexible wall and the plane rigid wall, respectively. The magnitude of the force is obtained by formula (

Calibration of mesomechanical parameters has always been an important issue in PFC simulation because there is no specific relationship between the mesoscopic parameters and the macroscopic parameters. Based on the calibration of mesoscopic parameters in recent studies, the parameters are continuously adjusted by trial and error until the stress-strain curve, elastic modulus, peak strength, and laboratory test results are approximately the same [

Particle flow simulation parameters.

Radius ( |
Radius ratio ( |
Friction coefficient ( |
Normal stiffness ( |
Normal-to-shear stiffness ratio (_{)} |
Tensile strength ( |
---|---|---|---|---|---|

85-141 | 1.66 | 0.5 | 60 | 1.33 | 5 |

From Figures

Stress-strain curves of laboratory tests and PFC simulation.

Dry density is 153 g/cm^{3}

Dry density is 1.61 g/cm^{3}

Dry density is 1.66 g/cm^{3}

The relation curve between peak strength and confining pressure in PFC test

The volume strain of the tailing sample is the amount of change per unit volume of the sample. Based on the initial volume, volume compression serves as positive volume strain, volume expansion serves as negative volume strain, and the point where the slope of the axial strain and volume strain curve of is 0 is defined as the critical point of the shear expansion trend. The relationship between axial strain and volume strain under PFC numerical simulation is shown in Figure

The relation curve of axial strain and volume strain in PFC numerical simulation.

Dry density is 1.53 g/cm^{3}

Dry density is 1.61 g/cm^{3}

Dry density is 1.66 g/cm^{3}

In the PFC simulation, there is no dilatancy phenomenon on the sample with a confining pressure of 100 kPa and a dry density of 1.61 g/cm^{3}, which is not consistent with the result of a slight dilatation phenomenon in Figure ^{3}.

Coordination number is an extremely important index in particle flow simulation, which is used to evaluate the degree of good contact between particles and compactness of a particle system. In this paper, the coordination number in the loading process is monitored by setting a measuring ball with a radius of 17 mm at the center of the model, as shown in Figure

Measuring ball diagram.

Coordination number changes of different dry density models during loading.

When the confining pressure was 100 kPa, the change of coordination number of different dry density models during loading showed that the initial coordination number of each dry density model was large, indicating good contact between particles in each model. With the loading process continued, the coordination numbers of different dry density models showed a trend of first increasing and then decreasing, and in the whole loading process, the coordination numbers of models with higher dry density were larger than those with lower dry density. When the dry density was 1.66 g/cm^{3}, the coordination number of the models decreased greatly at the later stage of loading, which may be because the samples with high dry density and low confining pressure were more prone to dilatation. The radial expansion of the model reduced the numbers of contact between particles, and the coordination number decreased significantly.

When the confining pressure is 100 kPa, the velocity vector diagram corresponding to different axial strains in the loading process is shown in Figure ^{3} dry density.

Velocity vector diagram of various axial strain sample under different dry density.

When the confining pressure is 100 kPa, the contact force between particles corresponding to different axial strains in the loading process is shown in Figure ^{3} and the axial strain was 15%, the particle contact force within a certain range near the side wall of the model decreased significantly, which may also be due to the phenomenon of dilatancy in the high-density model under low confining pressure.

Contact forces between particles of axial strain samples under different dry densities.

Based on the laboratory consolidated-undrained triaxial compression experiment, PFC is used to conduct numerical tests on tailings with different dry densities, and the fish language is used to monitor the stress, strain, peak strength and coordination number, particles velocity, and contact force between particles of the sample. Following conclusions are drawn:

By comparing the laboratory test with the PFC triaxial compression simulation test, the stress-strain curve, peak strength, and elastic modulus of the numerical simulation of each dry density tailing sample under different confining pressures and the laboratory test are in good agreement

Compared with the case of high confining pressure, the numerical test at low confining pressure has a higher degree of coincidence with the laboratory triaxial compression test. This is due to the assumption that particles are rigid and incompressible in PFC. However, the greater the confining pressure, the greater the degree of particle crushing and deformation in laboratory test

Under large confining pressure, the sliding and rotation of the particles inside the sample are restricted, suppressing the dilatancy of the sample

The initial coordination number of the numerical model is large, which proves that the contact degree of the model is good to some extent

In the triaxial numerical test, with the strain increases to a certain extent, the core area of the models bears most of the axial pressure

Both macroscopic and mesoscopic studies have proved that due to the close arrangement of high-density particles, the restraint force is small and the sample will tend to expand radially as loaded to a certain degree due to the slip and rotation between particles

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The authors declare no conflicts of interest.

This work is supported by the National Natural Science Foundation of China (51774187 and 51804164); the Research Foundation of Education Bureau of Hunan Province (17A184); and the Natural Science Foundation of Hunan Province (2019JJ50498). Thanks to Hunan Province Engineering Technology Research Center for Disaster Prediction and Control on Mining Geotechnical Engineering (2019TP2070) for providing experimental platform support and thanks to the Central South University.